simplify theta(sin theta) ²/2tan theta​

Answer:

Calculated value of F = 0.0535

The critical region is F >F ₀.₀₅ (6,21) = 2.575

Reject H0

Step-by-step explanation:

1. Null hypothesis

H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither

2. Alternative hypothesis

H1: Not all means are equal.

3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6

4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7

= 21

5. The significance level is set at α-0.05

The critical region is F >F ₀.₀₅ (6,21) = 2.575

The test statistic to use is

F = sb²/ sw²

Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom

Correction Factor = CF = Tj²/n = (410)²/28= 6003.57

Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43

Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 =  1.57286

Within SS = Total SS - Between SS= 104.43- 1.573= 102.86

The Analysis of Variance Table is

Source Of                 Sum of          Mean              Computed

Variation          d.f     Squares       Squares               F

Between

Samples          6         1.57286       0.2621               0.0535

Within

Samples         21       102.86           4.898

Calculated value of F = 0.0535

Pvalue = 2.575

Since it is smaller than 5 % reject H0.

Hello, please consider the following.

We know the following, right ?

[tex](\forall a, b \in \mathbb{R}) \left( sin(a+b)=sin(a)sin(b)+cos(a)cos(b) \right)[/tex]

So, here, it gives.

[tex]Asin(\omega t+\phi)=Asin(\phi){\sf \bf sin(\omega t)}+Acos(\phi){\sf \bf cos(\omega t)}\\\\=c_2{\sf \bf sin(\omega t)}+c_1{\sf \bf cos(\omega t)}\\\\\text{ *** where }c_2=Asin(\phi) \text{ and } c_1=Acos(\phi) \text{ ***}[/tex]

Do not hesitate if you need further explanation.

Answer:

  [tex]\displaystyle A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta[/tex]

Step-by-step explanation:

The shaded area is the area of the curve bounded by θ = π and θ = 7π/6.* A differential of area in polar coordinates is ...

  dA = (1/2)r^2·dθ

So, the shaded area is ...

   [tex]\displaystyle\boxed{A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta}[/tex]

_____

* We found these bounds by trial and error using a graphing calculator to plot portions of the curve.

Answer:

x≥4

Step-by-step explanation:

The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

5 - 2x ≤ -3.

Solve the inequality,

Add 3 to both the sides,

5 - 2x + 3 ≤ -3 + 3

8 - 2x ≤ 0

-2x  ≤ -8

Multiply -1 both the sides,

2x ≥ 8

x ≥ 4

The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).

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Answer:

Length of shortest side: 57

Length of medium side:59

Length of long side: 119

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

4x + 10 = 2(2x + 5)

Distribute

4x+10 = 4x+10

Since the left side is identical to the right side, there are infinite solutions

4x - 5 = 4x + 10

Subtract 4x from each side

-5 = 10

This is never true, so there are no solutions

4x-5 = -5

Add 5 to each side

4x = 0

x=0

There is one solutions

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Hello, there!!!

Let ABC be a Right angled triangle,

where, AB = 3

BC= 10

and AC= x

now,

As the triangle is a Right angled triangle, taking angle C asrefrence angle. we get,

h= AC = x

p= AB = 3

b= BC= 10

now, by Pythagoras relation we get,

[tex]h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]

[tex]or ,\: h = \sqrt{ {3}^{2} + {10}^{2} } [/tex]

by simplifying it we get,

h = 10.44030

Therefore, the answer is x= 10.

Hope it helps...

Answer:

[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer =  A.  Aella

Step-by-step explanation: Add 60, 25, and 95 degrees because that will equal 180 which is what the triangle equals.

Answer:

5/36 ; 1/12 ; 2/9 ; yes

Step-by-step explanation:

Given the following :

Roll of two fair dice : green and red

Probability = (number of required outcomes / number of total possible outcomes)

(a) What is the probability of getting a sum of 6?

Number of required outcomes = 5

P(sum of 6) = 5/36

b.) What is the probability of getting a sum of 10?

Number of required outcomes = 3

P(sum of 10) = 3 / 36 = 1/12

c.) What is the probability of getting a sum of 6 or 10?

P(getting a sum of 6) + P(getting a sum of 10)

(5/36) + (1/12) = (5 + 3) / 36

= 8/36 = 2/9

The events are mutually exclusive because each event cannot occur at the same time.

Answer:

x=-17/5

Step-by-step explanation:

–5(–2x – 5) – 2 – 1= -12

+10x+25-2-1=-12

10x+22=-12

10x=-12-22

10x=-34

x=-34/10

x=-17/5

Step-by-step explanation:

Open the brackets

10x +25 -2 - 1= -12

Collect the like terms

10x = -12-25+2+1

10x = -34

Divide both sides by 10

Therefore,x = -34/10 = -3.4

95% interval would be 95% of the population mean.

The answer should be:

A. 95% of the intervals constructed using this process based on samples from this population will

include the population mean

Answer:

A

Step-by-step explanation:

A 95% confidence interval indicates that 95% of the intervals constructed using this process based on samples from this population will

include the population mean

Answer:

maaqqqf aku ngak tau soal jawaban in

The perimeter of a shape is the summation of the visible lengths of the figure. The area; however, is the product of the length and the width of the figure

The perimeter of the figure is 58 units and the area of the figure is 130 unit square

Your question is not properly formatted and the diagram required to solve the question is missing. I've included the appropriate diagram.

Having said that, the perimeter is:

Perimeter = sum of all sides

[tex]Perimeter = 7 + 8 + 5 + 8 + 3 + 6 + 3 + 5 + 7 + 6[/tex]

[tex]Perimeter = 58[/tex]

To calculate the area, we use a different approach.

First, we split the figure into 3, we then calculate the area of each sub-figure, and then we add up the calculated areas.

From left to right, we have:

Rectangle 1

[tex]Length = 7\\Width = 6[/tex]

Rectangle 2

[tex]Length = 5\\Width = 6+8 = 14[/tex]

Rectangle 3

[tex]Length = 3\\Width = 6[/tex]

The area of a rectangle is:

[tex]Area = Length * Width[/tex]

So, the area of the figure is:

[tex]Area = 7 * 6 + 5 * 14 + 3 * 6[/tex]

[tex]Area = 130[/tex]

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Answer:

Prove:

Using 1

n³+2n = (1)³+2(1) = 1+2= 3 ---> 3/3= 1 ✔

Using 2

n³+2n = (2)³+2(2)= 8+4=12 --> 12/3=4✔

Using 3

n³+2n= (3)³+2(3)= 27+6= 33 --> 33/3=11✔

So it is proven that n³+2n is divisible by 3 for every positive integer.

I hope this helps

if u have question let me know in comments

Answer:

x = 58

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

90  = 32+x

Subtract 32 from each side

90-32 = x

58 =x

9514 1404 393

Answer:

  2.5 m/min

Step-by-step explanation:

To find meters per minute, divide meters by minutes:

  (7.5 m)/(3 min) = 2.5 m/min

The speed of the tortoise is 2.5 meters per minute.

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

Hunda expected stock price in 7 years = RM48.12

Step-by-step explanation:

expected year end dividend = RM1.60

required return = 11%

dividend yield = 6%

growth rate = constant

Determine Hunda corporation's expected stock price in 7 years

stock price in 7 years

= expected year end dividend / (required return rate - dividend yield rate )

= 1.6 * (1.06)^7  / ( 0.11 - 0.06 )

= 2.4058 / 0.05 =  48.12%

Answer:

The system is dependent:

x=-3t-7

y=-5t-15

z=t

Step-by-step explanation:

I chose to use a matrix to solve this system of equations. Once put into matrix form, you need to row reduce the system into its simplest form (Row Reduced Echelon form). Doing this, we find that the system is dependent on the z variable. And following usual procedures, we let z equal some other letter; which is t in this case. Then we isolate each variable to get the answer.

Check the attachment for the work.

[The arrows indicate a row swap and the parenthesis indicates addition if a constant multiple of one row to another]

Step-by-step explanation:

You're going to break√12 into ✓4 and √3 because 4*3 = 12. Square rooting 4 will give you two, and now you can add since the argument of the roots are the same.

Answer:

option C is best.

Step-by-step explanation:

y=a(x-h)^2+k

y-k=a(x-h)^2y

y-k/(x-h)^2=a

Answer:

|88-x| ≤ 14

Step-by-step explanation:

their score has to be within 14 points of 88.

if their score is above 88, the number will be negative, but the absolute value makes the number positive. if that number is still within 14 of 88, they pass.

if their score is below 88, the number will be negative, and the absolute value keeps the number positive. if that number is still within 14 of 88, they pass.

Answer:

19- 2(xy+yz+xz)

20- 16t(5-t)

Step-by-step explanation:

19) factor 2xy+2yz+2xz

2xy+2yz+2xz

=2(xy+yz+xz)

20) factor -16t^2 +80t

=80t-16t^2

=16(5t-t^2)

=16t(5-t)

Answer:

Hello,

19

Step-by-step explanation:

2 methodes:

1)

[tex]y=-4x^2+20x-6\\\\=-4(x^2-5x)-6\\\\=-4(x^2-2*\dfrac{5}{2}*x+\dfrac{25}{4} ) +25-6\\\\=-4(x-\frac{5}{2} )^2+19\\\\Maximum\ =19 \ if\ x=\dfrac{5}{2} \\[/tex]

2)

y'=-8x+20=0 ==> x=20/8=5/2

and y=-4*(5/2)²+20*5/2-6=-25+50-6=19

finding maximums/minimums in quadratic equations:

The maximum value is 19

We want to find the maximum value of:

y = -4z^2+20z-6

Here, you can see that we have a quadratic equation with a negative leading coefficient.

This means that the arms of the graph will go downwards. From this, we can conclude that the maximum will the at the vertex (the highest point).

Remember that for a general equation like:

y = a*x^2 + b*x + c

The x-value of the vertex is:

x = -b/(2a)

(you can see that the variable is a different letter, that does not matter, is just notation)

Then for our equation:

y = -4z^2+20z-6

The z-value of the vertex is:

z = -20/(2*-4) = -20/-8 = 5/2

Then the maximum of the equation:

y = -4z^2+20z-6

is that equation evaluated in z = 5/2

So we get:

y = -4*(5/2)^2 + 20*(5/2) - 6  = 19

The maximum value is 19

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Answer:

Step-by-step explanation:

The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;

Making C the subject of the formula from the expression given.

[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]

Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;

[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]

Hence the cost of goods sold is $960,000